Cubature formulas for two-variable functions with large gradients in the boundary layers

There are constructed and investigated the cubature formulas in the rectangular domain to compute the integral from a function of two variables with large gradients in boundary layers. It is assumed that the function have two components with large gradients which are known up to the multiplier. This components responsible for growth of function in boundary layers. Research is relevant, because the application of cubature formulas based on Lagrangian interpolation in the presence of large gradients leads to significant errors. Cubature formula with a given number of nodes in each direction is constructed. Formula is exact for selected components. It is proved that the error estimates of constructed formulas don't depend on large gradients of function in boundary layers.